The specific approach of using microelectronic fabrication techniques to produce microelectromechanical systems (MEMS) has led to mostly planar parts having dimensions in the vertical direction of only a few micrometers, many other techniques are being developed and applied to make multi-scale 3D devices. Although these methods have yielded primarily experimental devices up until now, many researchers and practitioners believe that multi-scale 3D devices, whose components range in size from several millimeters to micrometers and down to nanometers, will have a much greater application range than MEMS in many industries including medicine, communications, defense, aerospace, consumer products, and many more. Experts in the field agree that existing devices have limitation barriers that may impede further innovation. The barriers can be broadly categorized into three areas: 1) design and fabrication, 2) metrology and testing, and 3) assembly and packaging.
Ultra precision motion control devices, e.g. piezo actuators, are extensively used in positioning and alignment schemes requiring the highest precision. These devices have internal control loops equipped with sensors that render ultra high resolutions. To achieve multi-degree-of-freedom actuation, very often multiple translational and/or rotational actuators are simply cascaded, and based on a pre-calibrated kinematic coordinate transformation between each actuator sensor coordinate frame (SCF) and the object coordinate frame (OCF), the desired position and orientation with respect to the OCF are commanded to each actuator. When dealing with dimensions of sub-micrometer range, small pre-calibration errors, such as those resulting from non-orthogonal transducer axes, can lead to erroneous results. Especially in the case that rotational motion is necessary, the effects of pre-calibration errors in terms of geometries and dimensions become very significant. Error sources such as thermal expansion and sensor drift can be even more critical and will attribute to system time variance with respect to the OCE which necessitates a different means of compensation.
In this respect, visual feedback can provide a direct measure of position and orientation with respect to an OCF and defines a common reference frame to which multiple objects are registered, revealing the relative position and orientation between objects that are subject to relative positioning and alignment. A robust solution is to acquire real-time visual feedback from the object space which continuously compensates for various time varying error sources. Furthermore, in addition to pre-calibration and time variant error sources, a major obstacle in the case of micro-manipulation is the uncertain mechanics of the micro-domain. They are surface forces which are a combination of Van der Waals forces, electrostatic surface charges and other forces that occur at the micro-level and that overwhelm the effect of gravity. Models of interaction forces and actuation schemes based on them have been proposed, however it is still maintained that visual feedback from the working domain combined with intelligent control schemes are the most robust solution.
Using visual feedback from optical microscopes to control micro-manipulation processes has been investigated by several researchers for applications in both the engineering and the bio-medical field. For most work done in this area, true real-time visual servoing only involves two degrees-of-freedom (DOF), i.e. x and y, within the focus plane of the microscope; a natural consequence due to the narrow depth of focus of an optical microscope. Proposed methods of recovering the third DOF, i.e. z, inside the framework of visual servoing under a microscope are as follows. Using stereoscopic techniques to recover depth was proposed. Depth recovery using active vision techniques such as Depth from Focus, and methods using active illumination with triangulation were also proposed. However each of these methods requires some sort of mechanical scanning or requires intensive computation which inherently limits its ability to deliver real time information in the z-direction. Moreover, the achievable depth resolution of all these methods is coupled with the lateral resolution of the image obtained by the optical microscope, which is limited by diffraction. This ultimately limits the achievable vertical resolution and causes a trade-off between field of view and the vertical resolution of the system.
Interferometric methods such as Phase Shifting Interferometry (PSI) and Vertically Sampled White Light Interferometry (V-SWLI) can achieve vertical resolutions in the nanometer range without the dependence on lateral resolution of the optics.
Vertically Sampled White Light Interferometry (V-SWLI) is emerging as a powerful tool for high precision, high speed, non-contact depth recovery of various technical and biological specimens. While PSI achieves higher resolution, V-SWLI maintains the advantages of interferometry, while overcoming important limitations, such as height ambiguity, limited measurement range, and the requirement of surface roughness, inherent in conventional PSI. V-SWLI is briefly discussed as it serves as a foundation for L-SWLI in many respects.
In SWLI, a broad band light source is used with an interferometer microscope. FIG. 1-(A) shows a schema of a Mirau-type interferometer microscope setup. The white light source is amplitude divided at the beam splitter 2 (FIG. 1-A), one path reflects off the reference plane and the other off the sample object, the two paths are recombined hence interfering with each other and the interference for each sample object point is detected at the CCD array. For V-SWLI measurement, either the object or the reference plane is scanned incrementally along the direction of the optical z-axis. Interference fringes occur only when the optical path difference (OPD) of the two arms of the interferometer are smaller than the coherence length. A pixel-intensity time history, called an interferogram, is sampled for each pixel of the CCD array plane while the OPD is changed incrementally. An interferogram during a 20 μm scan is shown in FIG. 1-(B). The interference is extremely localized, generating a sharply defined coherence region that is only a few micrometers wide. The rest of the distribution represents low-frequency background illumination that stems from test surface scatter and defocus. The interferogram is constituted of a periodic signal modulated by an envelope function and can be simply modeled as,s(z)=B(z)±m(z−z0)cos(2πfz·z+θ)  (1)where m(z−Z0) is the envelope function, B(z) is the background illumination, fz is the carrier frequency and θ is phase. In order to obtain the height distribution, each interferogram of each pixel is processed to find the peak of m(z−zo), where the OPD of the two arms of the interferometer equal each other.
P. J. Caber proposed a method of demodulating the sampled interferogram to acquire the peak of the envelope function, which is explained briefly. The first step is to high-pass-filter the signal to get rid of low-frequency background illumination to get,s′(z)=m(z−z0)cos(2πfz·z+θ)  (2)The signal is then rectified, i.e. squared, in the second step, in effect doubling the carrier frequency,
                                          s            ″                    ⁡                      (            z            )                          =                                            1              2                        ⁢                                          m                2                            ⁡                              (                                  z                  -                                      z                    0                                                  )                                              +                                    1              2                        ⁢                                          m                2                            ⁡                              (                                  z                  -                                      z                    0                                                  )                                      ⁢                          cos              ⁡                              (                                                      4                    ⁢                    π                    ⁢                                                                                  ⁢                                                                  f                        z                                            ·                      z                                                        +                                      2                    ⁢                    θ                                                  )                                                                        (        3        )            
In this step, the second term of (3) is shifted away from the first one in the frequency domain such that the two can be easily separated by a suitable low-pass-filtering operation, which effectively isolates m2(z−z0)/2 for processing. Finally the peak of this function is located, and the vertical position that corresponds to the peak is recorded. To achieve depth resolution that is beyond the sampling interval, simple curve fitting operations can be performed, which result in a more accurate estimation of the peak position. Depth resolution of the current system is below 10 nm due to several factors, including optical dispersion, sampling accuracy, and the flatness of the reference mirror of the interferometer. A more thorough investigation into the resolution limiting factors is done in M. Fleischer's “Theoretical Limits of scanning white-light interferometry signal evaluation algorithm” Applied Optics, vol. 40 17, 10 Jun. 2001.